1. Field of the Invention
The present invention relates to a storage medium storing a computer program for determining at least one of exposure condition and mask pattern.
2. Description of the Related Art
In recent years, semiconductor devices have been miniaturized, which makes it more difficult to transfer (resolve) patterns in exposure apparatuses. Accordingly, the exposure apparatuses utilize super resolution technology such as off-axis illumination and optical proximity correction (OPC) to adapt to the miniaturization of semiconductor devices, and optimize a mask pattern or a shape of effective light source that illuminates masks. Japanese Patent Application Laid-Open No. 2009-302206 discusses a method of determining exposure conditions in view of either or both of exposure amount and defocus to acquire a desired image during exposure process.
In an exposure apparatus, each stage that supports a mask or substrate desirably stays at a predetermined position, but is known to be vibrating around the position with a slight amplitude in a cycle similar to or shorter than an exposure period. The vibration is likely to occur in each of the x, y, and z directions, where the z direction corresponds to an optical axis direction of a projection optical system, and the x and y directions are perpendicular to the z direction and correspond to the directions in which a stage moves. In a scanning exposure, a mask stage and a substrate stage ideally synchronize with each other during scanning, but practically they are a little bit out of synchronization. The vibration and asynchrony of the stages can be referred to as moving standard deviation (MSD).
When MSD occurs, while a single point on a substrate is exposed, a image is formed laterally shifted, or the plurality of laterally shift images are superimposed upon one another, which makes the resulting images, such as resist images (latent images) on a wafer, blurred. In addition, in the case where a projection optical system causes distortion, a plurality of images are formed laterally shifted and superimposed upon one another in scanning exposure, forming blurred images, as in the case of MSD.
The inventor of the present invention found that MSD often considerably affects the shapes of resulting images. In the prior art, however, no consideration is given to the effect of MSD onto the lateral shift of images in the methods of determining exposure conditions and mask patterns. Consequently, exposures based on the exposure conditions or mask patterns that are obtained only by optimization calculations do not provide adequate images as expected.